The diagonal of a rectangular field 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides the field.

Explanation

Let, ABCD be the rectangle
and Shorter side BC=x meter
`because` Diagonal AC= (x-60) m
and longer side AB=(x+30) m
Now, in `DeltaABC` by Pythagoras theorem
`(x+60)^(2)=(x=+30)^(2)+x^(2)`
`impliesx^(2)+120x+3600=x^(2)+60x+900+x^(2)`
`impliesx^(2)-60x-2700=0`
`impliesx^(2)-(90-30)x-2700=0`
`impliesx^(2)-90x+30x-2700=0`
`x(x-90)+30(x-90)=0`
`implies(x-90)(x+30)=0`
`impliesx-90=0orx+30=0`
`impliesx=90" "(because"sind cannot be negative")`
Hence, breadth of rectangle = 90 m and length =90+30=120 m.